Sampling for plant disease incidence

Knowledge of the distribution of diseased plant units (such as leaves, plan ts, or roots) or of the relationship between the variance and mean incidenc e is essential to efficiently sample for diseased plant units. Cluster samp ling, consisting of N sampling units of n individuals each, is needed to de termine whether the binomial or beta-binomial distribution describes the da ta or to estimate parameters of the binary power law for disease incidence. The precision of estimated disease incidence can then be evaluated under a wide range of settings including the hierarchical sampling of groups of in dividuals, the various levels of spatial heterogeneity of disease, and the situation when all individuals are disease free. Precision, quantified with the standard error or the width of the confidence interval for incidence, is directly related to N and inversely related to the degree of heterogenei ty (characterized by the intracluster correlation, rho). Based on direct es timates of rho (determined from the theta parameter of the beta-binomial di stribution or from the observed variance) or a model predicting rho as a fu nction of incidence (derived from the binary power law), one can calculate, before a sampling bout, the value of N needed to achieve a desired level o f precision. The value of N can also be determined during a sampling bout u sing sequential sampling methods, either to estimate incidence with desired precision or to test a hypothesis about true disease incidence. In the lat ter case, the sequential probability ratio test is shown here to be useful for classifying incidence relative to a hypothesized threshold when the dat a follows the beta-binomial distribution with either a fixed rho or a rho t hat depends on incidence.